Author: Debjyoti Bardhan

The US is burying the Cold War hatchet and doing so in style. It is dismantling the most powerful nuclear bomb ever created, believed to be over 500 times more powerful than the one dropped on Hiroshima. It was designed and armed in 1962, but, thankfully, never used. Named enigmatically as B53, it was to be carried by B-52 bombers and was capable of ripping apart even underground bunker facilities, should the Cold War have heated up.

The B53 at the Pantex Plant (Courtesy: Associated Press)

The B53

The B53 was a monster. It weighed in at 10,000 pounds (or 4.5 tonnes) and could release 9 megatons of TNT energy (or 38 PJ, 1 PJ = 1015 J a million billion joules)!! It formed a formidable arsenal, consisting of 340 individuals of its kind, built for B-47, B-52 and B-58 bomber planes. It used highly enriched Uranium (oralloy). It was meant to be used as a bunker buster a surface blast would send shockwaves that would shatter the Earth, enabling the underground parts to be exposed. Multiple strikes(!) would eliminate technical facilities or even the leadership bunkered underground.

Disarmament

The disassembling process for the B53 arsenal began in 1980’s, but a few of them kept their place in the stockpile. In 1997, it was decided to retire them from the arsenal. The process took longer than expected, because the technology was old and most of the experts are either old or deceased. It took place at the Pantex plant at Amarillo, Texas, the only plant for disarmament in the US.

The disarmament is considered complete when the 300 pound explosive the fuse is separated from the highly fissile nuclear material. This nuclear material is known as the pit and is not heavy enough to detonate on its own (technically, it is of sub-critical mass). These pits are stored at the plant, then sanitized’ and disposed off.

The Pantex plant has served as a disarmament facility for a number of nuclear bombs. It will continue to do so!

The secret of the 75,000-character “Copiale Cipher” is finally out! The manuscript is an enigmatic cryptic document, meticulously encrypted by a group of people believed to belong to a 18th century secret German society. The characters are a mix of Roman letters and abstract symbols. It was finally broken by an international team of cryptographers.

The Brute Force Approach … and “Complete Failure”

The manuscript, clad in a green and gold embroidered cover (pic above), was found in East Berlin Academy after the Cold War. Leading the effort was computer scientist Kevin Knight of USC Viterbi School of Engineering. He programmed his computer to track the occurrences of different commonly-occurring set of letters, aiming to find patterns and extract the grammar. The distribution of Roman and Greek characters was also a clue to the puzzle. Or so they thought.

As Knight says, this brute force approach,

took quite a long time and resulted in complete failure

Success!

After many such frustrating efforts, they completely eliminated the Roman characters, realizing that these were meant to mislead. The team then painstakingly tried to associate modern German consonants and vowels to different symbols or symbol groups. This finally made sense. The first clear phrase in German meant: Ceremonies of Initiation. What better could you have hoped for when translating the text of a secret society?

Try Your Hand

We present a conversion table for the symbols.

Now, we present a few pages, just to give you a glimpse of what the cryptographers were up against!

First one:

Next one:

The last one

Notice the large number of Greek letters

Concluding Words

Knight, who is a world-renowned translation expert and coder extraordinaire, has designed many translation software packages that have been adopted by companies like Apple and Intel. He says:

Translation remains a tough challenge for artificial intelligence.

As long as the Babel fish doesn’t evolve or is not intelligently designed, speaking a completely abstract language shall remain a great human fascination.

The mystery deepens. Scientists have found distribution of dark matter in dwarf galaxies, which is completely anomalous to the current theory of cold dark matter distribution in the Universe. The AMS observation from aboard the ISS has shown that dark matter is spread uniformly throughout the dwarf galaxy, whereas one would expect it to clump around the centre and then thin around towards the edges. This pattern, based on the prediction of the cold dark matter model, is seen in bigger galaxies like our own. Dwarf galaxies provide an exception and no one knows why.

A web of dark matter throughout the Universe?

What really is Dark Matter?

Dark matter refers to the attractive positive density matter that supposedly makes up as much as 23%-26% of the Universe, as compared to the 4% of visible matter (all stars, planets, galaxies everything that we know about!). The rest is dark energy and it is the energy of the vacuum, tending to tear to Universe apart making it accelerate its expansion. Dark matter was proposed by Fritz Zwicky and was initially invoked to explain the high speed of the outer spirals of a galaxy. They were spiraling too fast to be held by gravity of the visible matter. An invisible matter, interacting only through gravity had to be present. Gradually, it was recognized that dark matter could explain other things as well, like the observed cosmic microwave background radiation, unexplained gravitational lensing etc. Matter is believed to reside in the space-time trough created by lumps of dark matter.

It is to explain the motion of such galaxies that dark matter was hypothesized in the first place

The most successful version of dark matter has been the cold dark matter’ model, which says that the dark matter particles, whatever they may be, are moving very slowly with respect to light.

The Study and an Anomaly

The study involved observing the Fornax and Sculptor galaxies, which orbit the Milky Way. These are dwarf galaxies and are thought to be primarily made up of dark matter. What was expected was that the center would be rich in dark matter and then the distribution would thin out towards the edges. What was seen instead, was a uniform distribution, confounding scientists to no end. Matt Walker, the leader for this study conducted by the Harvard-Smithsonian Center for Astrophysics, says

Unless or until theorists can modify that prediction, cold dark matter is inconsistent with our observational data.

Dark matter distributions can be inferred from the motion of stars. The presence of matter curves space and matter particles follow curves on this curved space, called geodesics. The geodesics would be significantly modified by the presence of dark matter. This gives an estimate to the dark matter present. The team investigated the motion of about 2000 stars and found this anomaly.

Matt Walker says

After completing this study, we know less about dark matter than we did before

It’s just the debris left behind by the famous Halley comet, but is enough to light the night sky up. The Orionid meteor shower is one of the most spectacular meteor showers that occur during the year. The shower will peak on the morning of 22nd October, but the broad maximum means that the shower lasts from the 20th of October to the 24th of October. This is widely considered to be a toned down version of the famous Perseid meteor shower.

The Radiant of the Orionids lie near Betelgeuse (red giant star) of the Orion constellation

The shower is so named since it appears to originate from near the Orion constellation. The radiant (the point from where the shower is seen to originate) lies near the red giant star Betelgeuse in Orion (pic above).

When and What to Watch for

This time’s show should be a spectacle, given that the moon will be at its crescent stage and near the horizon at the peak of the shower. The best time to watch for the shower will be around 1:00 AM, while the moon peaks at about 2:00 AM EST.

The Orionid consists of tiny particles of debris from the parent comet of the size of sand grains. This is the trail of rubble that the Halley comet leaves behind as it makes an orbit around the Sun. The shower happens when the Earth moves through this trail. The dust falls’ through the atmosphere igniting due to the friction with the Earth’s atmosphere and causes streaks, which last for some time. These are popularly misnamed Shooting Stars’.

Prolific and long lasting

The Orionid shower is expected to produce about 20 meteors per hour on average, with the maximum likely hitting even 40 per hour, making this one of the most prolific meteor showers. However, due to the smallness of the burning pieces of debris, the shower will be drowned out by any light pollution close to your point of observation.

The signature of the Orionids is the long-lasting trails and the high speed of the particles.

You need not worry if you fail to catch the shower on the morning of 22nd October. You’ll have a chance on the 23rd and 24th as well, but the frequency will be going down steadily. Technically, the shower continues till the first week of November, but you’ll be able to see only a few stragglers’ streaking across the sky.

Europe is all set to launch the Galileo satellites its answer to the US GPS and Russian GLONASS on Friday, 21st October. The launch was supposed to have taken place early today (i.e. on 20th October), but unforeseen situations forced the launch to be shifted the next day. The satellites, a joint venture between European Space Agency and Roscosmos, will be launched using the Russian Soyuz rockets, marking the first use of Soyuz to launch a non-Russian payload.

Galileo placed on dispenser (Courtesy: ESA)

Self-Reliance is the Keyword

The Galileo system will free up the European nations from their reliance on American technology for a reliable tracking system. The US GPS is available to all, but it can be discontinued or restricted in times of war. If not completely barred, the precision of the service might also be curtailed by the US. The US GPS is ultimately controlled mainly by the US military, which holds very high priority in the policy making corridors of America. Galileo will free Europe of all such constraints.

Galileo will provide both high precision and low precision services. The low precision facilities will be open to all. The high-precision facilities will be used primarily by the military.

Galileo on the Soyuz Composite (Courtesy: ESA)

Features of Galileo

Navigational and Search-And-Rescue facilities

The Galileo system has some really great features, as compared to the US GPS and the Russian GLONASS. It will be an array of 30 satellites (27 active ones and 3 spares) all in an orbit about 23,000 km above the Earth’s surface. The navigational precision of Galileo is rumored to be better than the US GPS, though the exact numbers are not yet known. Galileo will also be able to do Search-And-Rescue (SAR) operations. Users can send distress calls along with their positions via the Galileo system to emergency agencies. Galileo has the additional facility of user feedback it will tell the user whether the rescue team has been deployed or not and what their location might be.

Time measurement facility

Galileo will fly up with four high precision atomic clocks of two types. The first type is a hydrogen based maser clock, which is accurate to 0.45 ns in 12 hours (i.e. it slows down by 0.45 nanoseconds in 12 hours!!). the clock uses the super-stable 1.4 GHz hydrogen atom transition line to measure time. The second type of clocks – Rubidium clocks – serves as back-up. The Rubidium clock is accurate to within 1.8 ns over 12 hours. Ultra-precise time measurement is one of the fundamental necessities of a proper positional and navigational system.

Galileo on Soyuz Composite - another angle (Courtesy: ESA)

Friction with Big Brother: Did the US plan to shoot Galileo down?

The US apparently planned to even shoot the Galileo satellites using missiles, since it feared that the facility might be used for military purposes against it. Tempers have cooled down and, with ESA declaring that the satellites won’t be used for spying, the US has no problem with the launch of the Galileo systems.

Named after the first real scientist, Galileo Galilee, the satellites aim to do what the great man always wanted to teach self-reliance in the matter of knowledge and thought.

These are the kinds of people who periodically remind you what is really wrong with the world. Remember Harold Camping, the doomsday prophet who claimed that the Rapture will be on us on 21st May? Predictably nothing happened. However, that hasn’t stopped him from pulling off the stunt once again and saying that the world will end on the 21st of October, i.e. tomorrow. This time though, he adds a cautious probably’.

Lying with one hand on the Holy Bible? Oh, my!

Camping Out!

Camping, who owns California-based Family Radio’, is a Christian fundamentalist and is known for getting his May 21st Rapture Day Prediction grossly wrong. Ironically, he survived a stroke in June.

Family Radio had made a fortune during the lead-up to the May 21st prediction due to the obscenely large amounts of money donated’ to the channel by the large number of believers, who prayed for their own souls and those of near and dear ones. Jesus Christ was, however, reluctant to show himself after death for a second time, turning the Second Coming into a damp squib. Camping absconded for a few days, his money safely stashed away.

Now, he returns with a more cautious stance. The world might end, he says. While the conservatives might welcome his softer stance, this might actually affect his popularity more adversely than the failed prediction. The inevitable question that a hardliner will ask is this: How can he be a prophet and not be sure of his own prophecy? Other people, like yours truly, who is neither on the hard-line or conservative believers’ groups, might find this mildly quaint or positively irritating.

Merely Harmless Fun, Right?

The May 21st prediction wasn’t merely a cruel joke for many people. Many people actually quit their jobs, or sold all their belongings or calculated their last till that day. When the day passed without them being redeemed, they were literally reborn in a world bereft of everything they possessed. How is Camping not culpable of crime? The toned down build-up to this present event means that very few people will believe in it and, hopefully, no one will do the unthinkable.

This is one conspiracy theory that can boast of being out of this world literally. The comet Elenin, dubbed the Doomsday Comet’, is due to pass Earth on Sunday, 23rd October, 2011. The comet has been closely watched by skywatchers, both out of interest and out of fear of the conspiracy theories. Some claim that Elenin is really the planet Nibiru that is destined to bring doom on Earth.

The Elenin Comet - as seen in early September. The comet has disintegrated since then.

About Elenin

Elenin started to break up late August and continued to do so till early September, due to the increased solar activity. The closest approach distance of Elenin will be approximately 22 million miles or 36 million kilometers. Elenin will be a big disappointment for both conspiracy theorists and other sane people it won’t be apocalyptic and it’ll hardly be a light show either. The comet is broken up into fragments and these pieces will not be very visible as they stream across space.

The conspiracy theory is Elenin’s only claim to fame it is a disappointing little rock orbiting the Sun with a massively eccentric orbit (i.e. one that strays away from being a circle by a long margin) and a very long period (i.e. it takes a very long time to orbit the Sun). Elenin’s return, if it survives this current journey, is projected to happen after 12,000 years.

The orbit of Elenin

Apocalypse – or not quite

There have been and will be many Armageddon theories. Rest assured that the uneventful passing of this comet will not quell the frequency of these theories. You can also be sure of the fact that this is unadulterated rubbish.

After Harold Camping and his great Doomsday prediction that spectacularly went bust, we have Nibiru (or Elenin, whichever you prefer). Everyone enjoys an apocalyptic fairy tale once in a while, right?

It’s about being ambitious and daring to be different. I interviewed the man who intends to solve the Riemann hypothesis, using quasi-crystals. I already wrote about it here and I strongly suggest that you go through that article before reading the interview.

In the interview, I ask him about his method of attack and his methodology of recruiting people for the expedition. He openly says that the journey is just starting. We end it with a light-hearted chat about his Twitter moniker and his email ID.

Here’s the full interview:

Me: Kindly say a bit about yourself. I know that you conducted a neutrino workshop a few days ago. Are you a mathematician interested in physics or a physicist interested in mathematics?

Rohit Gupta: Yeah, the workshop I conducted on neutrinos was about 2 months prior to the OPERA results going online. I was pretty sure that neutrinos were the ‘ghost’ in the standard model, and well – now everyone is talking about it.

About me, let’s just say that I am a cosmologist who is interested in connections between physics and number theory. My educational background is Chemical Engineering ( IIT Kharagpur, class of 99) and after that I have been mostly self-taught and self-employed.

Me: Cool! Yeah, I can’t resist the temptation. Just one more off-the-track question before the real questions. What’s your take on the faster-than-light neutrino results?

RG: I’m no experimental physicist, but even if you read the literature on the original neutrino experiments like Homestake or the SN1987 at Kamiokande, we are dealing with a jaw-dropping piece of work purely in statistical terms. OPERA is no more controversial than solar neutrinos were for about 30 years.

It is too early to take sides, but personally I will try to study the work of Ettore Majorana. That sounds promising. I don’t know it too well, though.

Me: Okay. First of the serious questions. You mentioned Erbium in your blog. You said that the energy levels would correspond to the pattern of zeros of the Riemann zeta function. Given that Erbium is large atom and cannot be solved exactly, how can you precisely know the energy levels? The zeros of Riemann Zeta are definitely well-defined and precise.

RG: I am not going by the experimental data Dyson is referring to, I am going after the idea itself. That has little to do with Erbium, that has to do with quasicrystals and the Riemann-Zeta. And Dyson is not my only inspiration, there are other lesser known papers, there’s one by Akio Sugamoto which models “factorization of integers into prime numbers viewed as decay of a particle into elementary particles conserving energy”. I think that is what excites me, that there is something corporeal behind numbers, a physical connection.

Me: And that precisely brings me to the next question.

I am curious about the quasi-crystal strategy you intend to employ. You mention that ” if the Riemann Hypothesis is true, then the zeroes of the zeta function form a quasicrystal”. Do you intend to ‘make’ a quasicrystal in 1-D and match it with the zeros of the R-Z function? Is a 1-D quasicrystal unique?

Further, can you be sure of the generality of the result? I mean, you cannot possibly compare all the zeros, right? How do you that the R-Z function follows the quasi-crystal to Re(s)->infinity?

Also, I’m quite surprised to think that this hasn’t been tried by someone else, especially when someone like Freeman Dyson had suggested it.

RG: There are gaps in the theory because quasicrystal theory is very new. What Dyson suggests as a first target is to classify quasicrystals in 1-D, a well-known example being the Fibonacci sequence. There are many such sequences and a classification of these requires a new metric. Once we have the metric, we find the one that corresponds to the Riemann Zeta. So yeah, I intend to make such a quasicrystal in 1D. Because the quasicrystal has a precise artificial structure, we can know for sure it corresponds to infinity.

I’m pretty surprised too that this hasn’t been given a serious attempt, and probably very lucky in that aspect.

Me: I have an objection there:

You say: Because the quasicrystal has a precise artificial structure, we can know for sure it corresponds to infinity.How do you know that the two follow each other till infinity? A trillion zeros have been found and all follow the Riemann hypothesis, but the jury’s still out because a generic proof has not been found. How are you so sure of the exact correspondence?

RG: I’d be able to answer that only once I have the structure of such a sequence. Only then can we say that it is a logical equivalent to (and implies) the Riemann Hypothesis. We haven’t even begun the actual expedition, we merely have a conjecture and a chance to fail heroically.

Me: Great! Let me now move from the method to the methodology.

You’re trying to recruit people for this expedition. I don’t understand how recruiting people not specializing in this will help. Do you really think they can contribute? You mention about teaching them the definition of ‘primes’. If that is the case, then what hope is there for the actual solution to the problem?

RG: My friend Edmund Harriss is a mathematician who has extensive experience with quasicrystals. You can see his opinion on the project here: http://maxwelldemon.com/tag/riemann-hypothesis/. There are more artists, designers and of course mathematicians who are slowly joining this. I welcome everyone.

I am asking people to share the journey with each other and learn a lot in the process by playing with it once I have explained it in a layman terms, the first three months is for that. Then there is a live GoogleDoc which the public can view ( but only the members can edit ) This public document will start from the basics and lead up to our attempt at solving the Riemann Hypothesis.

There are a few outcomes possible 1) The hypothesis is not provable 2) it is provable 3) it is not possible to know whether it is provable or not and 4) the proof exists but is too long by human standards. What then? That is an open question for future generations and only collaborative activity can resolve this.

Me:What do you think the consequences of the solution might be? Except for you getting immensely famous and obscenely rich, that is.

RG: HAHAHA…I hope so my friend, I’m tired of having to charge a fee for my workshops. But that aside, the longest existing proof is currently the “classification of finite simple groups” and that is tens of thousand of pages in hundreds of journals. I imagine that if we realize that a proof of the Riemann Hypothesis exists, but no single human being or even several generations can never read the one million, trillion or even more pages needed to verify it, we will have to create an entirely new system of collaboration in human society.

Me: Yes, the Enormous group classification proof is really enormous. Let’s end with something light-hearted.

RG: I once wrote a comic book called the Doppler Effect, where the protagonist is a creature called the Fadereu, who is only visible when he moves, or else he fades away in the air. It was my nickname for a long time, but when I got bored I kept changing it with my age. It’s here:

Special Relativity may have saved itself from disaster. According to a scientist, the OPERA collaboration overlooked a crucial correction to the result, which exactly matches the discrepancy observed. It involved the effect of time dilation of the clocks aboard the GPS satellite.

The two frames

Ronald Van Elburg says that the two frames of reference the Gran Sasso laboratory on the ground and the clocks on the GPS satellite in orbit around the Earth – are in relative motion with respect to each other and thus special relativity effects come into the picture. The time of flight, thus, needs to be corrected for this factor too.

From the perspective of the clock, the detector is moving towards the source and consequently the distance travelled by the particles as observed from the clock is shorter

Magnitude of the Effect

Now, for the crucial magnitude of this effect. Van Elburg presents the analysis which shows that this timing should account for 32 ns for the time of flight. Further, this happens at CERN as well as the Gran Sasso Lab in Italy and thus, the number has to be doubled, yielding 64 ns, which exactly compensates the noticed discrepancy of 60 ns.

This solution has recently been released and is yet to be verified properly. The effect seems too obvious and it seems unlikely that OPERA has not taken it into account. OPERA has not responded as yet.

A theoretical attack on the results

Recently, there has been a theoretical attack on the experimental result by Sheldon Glashow (Nobel Laureate, Physics) and his Boston University colleague, Andrew Cohen. They dismiss the results by showing that if the result were true, no high energy neutrino would reach the detector at Gran Sasso. The fact that they detect high energy neutrino (above 12.5 GeV) means that the neutrinos are not travelling faster than light. This is not an experimental result, but a theoretical bound.

We’ll just have to wait and watch. The van Elburg paper is a pre-print and is not yet peer-reviewed.

Rohit Gupta, an Indian Mathematician, is trying to solve a difficult math problem and he intends to get you involved too! The problem the Riemann Hypothesis – is one of the toughest problems ever and no one knows a solution to it yet. It regards the distribution of prime numbers on the real number line, but more of that in just a bit. More interesting is the person himself and his goal. He intends to use Quasi-crystals (this year’s Nobel recipient in Chemistry, by the way) to solve this so-far intractable problem. The call is out for anyone who wants to join him anyone really, whether a mathematician or not!

He not only plans to attack the problem, he wants to do so in public. To do that he’ll conduct workshops dubbed KNK103, with KNK standing for Kali and Kaleidoscope’. But, he points out, this isn’t just a workshop it’s much more, it’s a mathematical expedition’.

The Riemann Hypothesis: The Beast and the Legend around it

The Beast

The Riemann Hypothesis is probably the toughest Math problem known. We all know that prime numbers are scattered all over the number line, but we don’t know whether there is any pattern in this or not! The prime number theorem states that all prime numbers upto some integer n’ lie below a maximum line, given by different formulae.

The statement of the Riemann Hypothesis is easy enough to state all non-trivial zeroes of the Riemann Zeta function lie on the critical line whose real part is ½.What this cryptic statement means is difficult to explain. The Riemann zeta function is shown below, valid for only Real(s)>1. (Remember, s can be a complex number.)

The Zeta Function in the Complex Plane. It has a unique analytic continuation from the Real Number line to the entire Complex Plane.

The function has Analytic continuations, which are too technical to consider here. The analytic continuation has trivial zerosfor s=-2,-4 etc. There are also non-trivial zeros (i.e. where the value of the function vanishes) of the Riemann Zeta Functions (and its analytic continuation), apart from these zeros. The Riemann Hypothesis is that these zeros should lie on a line, whose real part is ½. Don’t worry if you’ve not understood much of this section, just keep reading.

Here’s a Mathematica demonstration of the Riemann Hypothesis

The Legend

The Riemann Hypothesis is listed at number 8 on Hilbert’s list of 23 greatest unsolved problems, and has on its head a prize of US$ 1 million, announced by the Clay Mathematical Institute. The hypothesis has been tested for 1 trillion zeros, but no general proof exists, i.e. how do you know there isn’t a zero that doesn’t lie on the Re(s)= ½ line beyond the trillionth zero?

The solution to the Riemann Hypothesis is thought to be a key step in many problems in topology, number theory and even cryptography. It is rumored that internet security will be revolutionized if the problem is solved.

Role of Quasicrystals!!

Here comes the most interesting part: Quasicrystals. Rohit Gupta wants to use quasi-crystals to attack the problem. He plans to use the energy levels in these crystals and look into the pattern to see if it fits the pattern of the zeros of the Riemann zeta function on the critical Re(s)= ½ line.

Quasicrystals - one of them

The idea is not new and he admits to being inspired by a conversation between Freeman Dyson and Hugh Montgomery. They noticed that the energy levels of heavy atoms, like Erbium, have energy levels which follow the pattern of the zeros of the Riemann Zeta function. Here’s Marcus du Sautoy’s account:

They discovered that if you compare a strip of zeros from Riemann’s critical line to the experimentally recorded energy levels in the nucleus of a large atom like erbium, the 68th atom in the periodic table of elements, the two are uncannily similar. It seemed the patterns Montgomery was predicting for the way zeros were distributed on Riemann’s critical line were the same as those predicted by quantum physicists for energy levels in the nucleus of heavy atoms. The implications of a connection were immense: If one could understand the mathematics describing the structure of the atomic nucleus in quantum physics, maybe the same math could solve the Riemann Hypothesis.

Yes!! Quantum mechanical solutions might already have solved the Riemann Hypothesis, loosely speaking. Gupta mentions If the Riemann Hypothesis is true, then the zeros of the Riemann Zeta function form a quasi crystal.Freeman Dyson said of this approach:

Suppose that we find one of the quasi-crystals in our enumeration with properties that identify it with the zeros of the Riemann zeta-function. Then we have proved the Riemann Hypothesis and we can wait for the telephone call announcing the award of the Fields Medal.

Who can participate in the grand project? How about you?

Gupta wants everyone to participate in this. He wants everyone from designers and copywriters to paranoid politicians and Polar bears with Polaroid Cameras (His own words)!

The introductory fee is Rs. 4900 (about $100) for lifetime. The workshops will be held online. There is no last date to register as the project is not time bound. He can be found on Twitter as @fadesingh and his gmail id is fadebox at gmail . com. You can register here.

I’ll use Freeman Dyson’s quote taken from Gupta’s page to finish this article: the history of mathematics is a history of horrendously difficult problems being solved by young people too ignorant to know that they were impossible.